In this paper, we study the distributed coordination and control of a set of asynchronous, anonymous, memoryless mobile vehicles that can freely move on a twodimensional plane but cannot communicate among themselves. In particular, we analyze the problem of forming a certain pattern and following a designated vehicle, referred to as the leader, while maintaining the pattern: the flocking proble...

Applying a microscopic model, we study theoretically the quasiparticle excitation of twodimensional topological insulator (TI) being in proximity to high-Tc superconductor. In momentum space, induced pairing term TI layer includes both singlet channel and triplet channel, leading C4 rotational symmetry breaking energy bands spectra. For cylinder geometry, zero edge states may appear but they ar...

Epistemic modal predicate logic raises conceptual problems not faced in the case of alethic modal predicate logic: Frege’s “Hesperus-Phosphorus” problem— how to make sense of ascribing to agents ignorance of necessarily true identity statements—and the related “Hintikka-Kripke” problem—how to set up a logical system combining epistemic and alethic modalities, as well as others problems, such as...

Cellular automata are considered to be a nice model of complex systems in which an infinite oneor twodimensional array of finite state machines (cells) updates itself in synchronous manner according to a uniform local rule. In this project report, we give an overview of our project. We have proposed a large number of algorithms for a variety of cellular automata. We focus our attention to the s...

We consider the following problem, arising within a geological model of sedimentationerosion: For a given vector field g and a given nonnegative function F defined on a oneor twodimensional domain Ω, find a vector field under the form g̃ = ug, with 0 ≤ u(x) ≤ 1 for a.e. x ∈ Ω, such that divg̃ + F ≥ 0 and (u − 1)(divg̃ + F ) = 0 in Ω. We first give a weak formulation of this problem, and we prove a...

The immersed boundary (IB) method is a computational framework for problems involving the interaction of a fluid and immersed elastic structures. It is characterized by the use of a uniform Cartesian mesh for the fluid, a Lagrangian curvilinear mesh on the elastic material, and discrete delta functions for communication between the two grids. We consider a simple IB problem in a twodimensional ...

Traditional analytic or controltheoretic solutions to the problem of optimizing evasive maneuvers in the extended two-dimensional pursuer/evader problem require the evader to execute specific sequences of maneuvers at precise pursuer/evader distances. These solutions depend upon several pursuer-specific characteristics, and fail to effectively account for uncertainty about the state of the purs...

A minimum-time Model Predictive Control (MPC) problem is considered. By employing a time scaling transformation and cost regularization, it is shown that this problem becomes amenable to the application of parametric Integrated Perturbation Analysis Sequential Quadratic Programming (IPA-SQP). The IPA-SQP framework exploits neighboring extremal optimal control and sequential quadratic programmin...

The aim of the study is to develop a finite element model postmortem heat exchange head in presence an open penetrating traumatic brain injury and assess degree its influence on temperature field this area body. Using ELCUT 6.5 application, based method, modeling geometry anatomical structures human absence wound associated intracranial membrane hemorrhages was carried out. A twodimensional fin...

We study the existence of minimizers for 2-dimensional ferromagnetism with various assumptions on different terms of the total energy. Our general philosophy for finding the minimizing magnetizations is to reduce this problem to a minimization problem for a new energy over a divergence-free field. Such a general philosophy works for all dimensions. However, in the twodimensional case, since the...